Nick: You are a rockstar. That is great. I am going to have to meditate on this.

Incidentally, I think you had mentioned at one point that Lannes had some general approach to the Sullivan conjecture that could be applied to give the Segal conjecture (i.e., it tells you how to calculate mapping spaces where the target is not finite). Does anything like that apply here?

Anyone got a reference for learning about configuration spaces in which particles are allowed to collide? I know there are a lot of things this can mean, but some kind of survey would be ideal.

Hm, it just occurred to me that singular braids have a funny thing you can do, which is replace singularities with OTHER braids... i.e. "blow up" singularities. I wonder if this corresponds to any kind of operad structure...

@user685252 I actually sort of take issue with the practice of giving millions of dollars to already well-employed and widely recognized mathematicians. Think of how many graduate student fellowships, or postdoctoral fellowships, or conferences, one could fund with that money.